Question

I have some question about relativistic features of objects which moves with speed of light.

If an object accelerates for infinite time, then it will in the end reach speed of light. Then, to make it clear, assume a rocket with infinite power source (source is also assumed to be massless) that accelerates in space, or vacuum without any disturbance in its motion. Also assume that there is another rocket same as the one mentioned above and, in vacuum, it moves with speed of light without any force given to it. Both move with speed of light relative to an observer at rest.

Sums up: From t=0, rocket A is accelerated until it reaches the speed of light and infinite and massless power source is assume to be given even after the speed of rocket A = c. Rocket B, on the other hand, at t=0, it moves with speed of light and moves forward in constant speed in vacuum.

What are differences in physical properties between two object?

Answer 1

# If you have a rocket with non-zero mass and if it moves at a speed of light (your 2nd rocket, Rocket B), then it's energy    would be infinite (which is practically impossible). But let's assume you have that.

# Now you have an infinite power source and you are accelerating another rocket (Rocket A). You are saying that, at time, t = infinity, your Rocket A would reach the speed of light. That's also a valid statement.

# Now, think carefully about what you mean by INFINITE (i.e. at time, t = infinity).

Infinity is not a number that you can reach there and you can go beyond that if you try harder.

Infinity is basically a sensation which says that how much you try you can never reach there (and going beyond that is out of question).

# So, you can never reach t = infinity.

This means, you can never have your Rocket A at the light speed (no matter how long you accelerate). (If you defend yourself by saying "ok, I will wait for infinite time and get my rocket at that speed", then I would say, go back again through the arguments of infinity and convince yourself that you can't.)

# So, you can never accelerate something and get it to the speed of light.

##### I think this will clarify your confusion and help you think physically.

# Now the difference in physical property of Rocket A and Rocket B:

[ I ] As Rocket B is in light speed, everything inside it don't evolve with time (i.e. time stops there), whereas time will run slow but never stops in Rocket A.

[ II ] To an outside observer, Rocket B would be contracted to a point whereas Rocket A always have finite length (which will tend to zero but never reaches zero). etc

## If you still stick to your question, then I would say there will be no difference in physical properties between two bodies with non-zero mass and light speed (which is again not physical). If they are of zero-mass then there property would depend on there energy, like photons with different energy have different frequencies.